My science teacher posed a challenging question that has me stumped! It goes like this: “Given that half the resistance of a power grid is 128.3456713 MΩ and a current of 30 tc over 26 hours, calculate the potential difference and show all your work.” Can anyone help me figure this out? 😭
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To find the potential difference across a power grid, we can use Ohm’s law, which states that:
[ V = I \times R ]
where:
– ( V ) is the potential difference (voltage),
– ( I ) is the current,
– ( R ) is the resistance.
Given:
[ R = \frac{128.3456713 \, \text{MΩ}}{2} = 64.17283565 \, \text{MΩ} ]
The current is given as 30 tc (where “tc” might be a typo for a unit of time), which possibly indicates a current of 30 A (assuming tc indicates Amperes, though please confirm).
The time provided is 26 hours, but since current is typically considered in seconds, we need to convert this time into seconds:
[ 26 \, \text{hours} = 26 \times 60 \times 60 \, \text{seconds} = 93600 \, \text{seconds} ]
Now that we have the resistance and the current (assuming it’s in Amperes), we can calculate the potential difference.
Calculation of Potential Difference:
Convert the resistance to ohms for easier calculation:
[ R = 64.17283565 \, \text{MΩ} = 64.17283565 \times 10^6 \, \text{Ω} = 64172835.65 \, \text{Ω} ]
Now plug the values into Ohm’s law:
[ V = I \times R = 30 \, \text{A} \times 64172835.65 \, \text{Ω} ]
[ V = 30 \times 64172835.65 \approx 1925185069.5 \, \text{V} ]
Conclusion:
Thus, the potential difference ( V ) across the power grid is approximately 1,925,185,069.5 volts or 1.93 billion volts.
Feel free to ask if you need further clarifications!